A type of integrated circuit referred to here as a “network flow processor” is a useful component in the design and manufacture of various types of networking equipment. For example, one particular prior art network flow processor integrated circuit has various processors and transactional memories, special processing circuitry and hardware engines, as well as ingress circuitry and egress circuitry. The transactional memories can perform several different atomic transactional memory operations, one of which is an atomic ticket release operation. To use the ticket release function of a transactional memory that has a ticket lock functionality, a processor passes the transactional memory a value in what is called an atomic “ticket release” command. This command is really a request to release. In response to receiving the ticket release command, the transactional memory compares the value carried by the command to a “next expected value” stored in a block of memory. If the value carried in the command is determined to match the next expected value stored in the block of memory, then the transactional memory outputs an indication of this. The value is said to have been “released”. In addition, the transactional memory also indicates how many, if any, subsequent consecutive values were previously flagged by the transactional memory as having been previously received in other ticket release commands where the previously received values were not “released”. The transactional memory outputs an indication that all such consecutive values should also be released. After outputting this information, the transactional memory updates the “next expected value” stored so that it points to the first value in the sequence of values that is not flagged. If, on the other hand, the value carried in the ticket release command is determined not to match the “next expected value” stored in the block of memory, then a bit in a bitmap maintained by the transactional memory is set to flag the fact that the out-of-sequence value was received, but that it was not released. The transactional memory is then available to process another atomic ticket release command. When the transactional memory outputs an indication of one or more consecutive values in response to a ticket release command, these values are said to have been “released”. This ticket release mechanism is a general purpose mechanism provided by transactional memories on one type of prior art network flow processor. The transactional memories also provide other general purpose mechanisms. In the prior art network flow processor, packets are received onto the integrated circuit, and pass through the ingress circuitry, and are classified as belonging to one of a plurality of groups of flows. In one example, packets of each such group of flows are processed by a separate software pipeline. Packets are put into the software pipeline for processing the proper order, so the packets are then output from the software pipeline in the proper order, or in roughly the proper order. The packets of such a group of flows then pass through the egress circuitry, including the reordering hardware circuitry of the egress circuitry, and pass out of the network flow processor. For additional information on this prior art network flow processor, as well as for additional information on transactional memories in prior art network flow processors in general, see: 1) U.S. Pat. No. 8,775,686, entitled “Transactional Memory That Performs An Atomic Metering Command”, by Gavin J. Stark, filed Aug. 29, 2012; and 2) U.S. Patent Publication Number 20140075147, having U.S. patent application Ser. No. 13/609,039, entitled “Transactional Memory That Performs An Atomic Look-Up, Add and Lock Operation”, by Gavin J. Stark et al., filed Sep. 10, 2012 (the entire subject matter of these two patent documents is incorporated by reference herein).